Let n be a fixed integer with n≥2. We say that two polynomials P and Q with real coefficients are block-similar if for each i∈{1,2,…,n} the sequences\begin{eqnarray*}
P(2015i), P(2015i - 1), \ldots, P(2015i - 2014) & \text{and}\\
Q(2015i), Q(2015i - 1), \ldots, Q(2015i - 2014)
\end{eqnarray*}are permutations of each other.(a) Prove that there exist distinct block-similar polynomials of degree n+1.
(b) Prove that there do not exist distinct block-similar polynomials of degree n.Proposed by David Arthur, Canada algebrapolynomialIMO Shortlist